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Hauptverfasser: Jaitly, Akshay, Jha, Devesh K., Ota, Kei, Shirai, Yuki
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:https://arxiv.org/abs/2509.26459
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author Jaitly, Akshay
Jha, Devesh K.
Ota, Kei
Shirai, Yuki
author_facet Jaitly, Akshay
Jha, Devesh K.
Ota, Kei
Shirai, Yuki
contents Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration constraints between objects, resulting in a non-trivial and computationally expensive problem. This makes the use of optimization-based methods for planning and control challenging. In this paper, we present a method to efficiently enforce non-penetration of sets while performing optimization over their configuration, which is directly applicable to problems like collision-aware trajectory optimization. We introduce novel differentiable conditions with analytic expressions to achieve this. To enforce non-collision between non-smooth bodies using these conditions, we introduce a method to approximate polytopes as smooth semi-algebraic sets. We present several numerical experiments to demonstrate the performance of the proposed method and compare the performance with other baseline methods recently proposed in the literature.
format Preprint
id arxiv_https___arxiv_org_abs_2509_26459
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Analytic Conditions for Differentiable Collision Detection in Trajectory Optimization
Jaitly, Akshay
Jha, Devesh K.
Ota, Kei
Shirai, Yuki
Robotics
Computational Geometry
Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration constraints between objects, resulting in a non-trivial and computationally expensive problem. This makes the use of optimization-based methods for planning and control challenging. In this paper, we present a method to efficiently enforce non-penetration of sets while performing optimization over their configuration, which is directly applicable to problems like collision-aware trajectory optimization. We introduce novel differentiable conditions with analytic expressions to achieve this. To enforce non-collision between non-smooth bodies using these conditions, we introduce a method to approximate polytopes as smooth semi-algebraic sets. We present several numerical experiments to demonstrate the performance of the proposed method and compare the performance with other baseline methods recently proposed in the literature.
title Analytic Conditions for Differentiable Collision Detection in Trajectory Optimization
topic Robotics
Computational Geometry
url https://arxiv.org/abs/2509.26459